Experimental study of the ${}^{38}\mathrm{S}$ excited level scheme

Information on the ${}^{38}\mathrm{S}$ level scheme was expanded through experimental work utilizing a fusion-evaporation reaction and in-beam $\gamma$-ray spectroscopy. Prompt $\gamma$-ray transitions were detected by the Gamma-Ray Energy Tracking Array (GRETINA) and recoiling ${}^{38}\mathrm{S}$ residues were selected by the Fragment Mass Analyzer (FMA). Tools based on machine-learning techniques were developed and deployed for the first time in order to enhance the unique selection of ${}^{38}\mathrm{S}$ residues and identify any associated $\gamma$-ray transitions. The new level information, including the extension of the even-spin yrast sequence through $J^{\pi }=8^{(+)}$, was interpreted in terms of a basic single-particle picture as well shell-model calculations which incorporated the empirically derived FSU interaction. A comparison between the properties of the yrast states in the even-$Z, N=22$ isotones from $Z=14$ to 20, and for ${}^{36}\mathrm{Si}–{}^{38}\mathrm{S}$ in particular, was also presented with an emphasis on the role and influence of the neutron $1p_{3/2}$ orbital on the structure in the region.

Figure 1

The energy of the first ion chamber section ($E_1$) plotted against the energy of (a), (b) the second section ($E_2$), (c), (d) the third section ($E_3$), and (e), (f) the dispersive position at the FMA focal plane ($x$). The time-coincidence gate $|\mathrm{\Delta }{T}_{\gamma -PGAC}|<200$ ns was applied to the gray-scale histograms which are the same across each row. Element ($Z$) labels in panels (a) and (c) identify the general regions of interest, while the white line identifies the central region covered by ${}^{38}\mathrm{S}$ recoils. The labels in panel (e) correspond to $A/q$ values. The overlaid spectra in panels (b), (d), and (f) include data which define the manual cuts (gray points) and from differing model output values, $k_{ml}>0.25$ (yellow), 0.60 (blue), and 0.81 (pink), as defined in Fig. 4 (see text for additional details). The white lines in panels (a)–(d) represent the central region of the S isotopes and are the same for each row.

Figure 2

The total spectrum of $\gamma$ rays encompassed within the manual gating regions (see text and Fig. 1). The labeled events used for the NN model training data set are distinguished by the colored regions. Note that for the labeling of the ${}^{38}\mathrm{Cl}$ and ${}^{181}\mathrm{Ta}\gamma$-ray transitions, a down-sampling of $\times 4$ was used, hence, their reduced size relative to the total counts in spectrum.

Figure 3

(a)–(d) The evolution of the distribution of model output values, $k_{ml}$, for the training data at snapshots throughout the NN model training at completed epoch cycles (1, 5, 10, and 100). Purple lines correspond to the $k_{ml}$ values of the labeled ${}^{38}\mathrm{S}$ training data and the black lines are the corresponding values of the sum of the ${}^{38}\mathrm{Cl}, {}^{33}\mathrm{P}$, and ${}^{181}\mathrm{Ta}$ labeled training data. (e)–(h) The fraction of the total number of integrated counts (given in %) over the integral range starting from the $k_{ml}$ value given on the $x$ axis through $k_{ml}=1$, i.e., ${\int }_{k_{ml}}^{1}dN/{\int }_0^{1}dN$.

Figure 4

The distribution of the model output values, $k_{ml}$, for the fully trained NN model ($\text{epochs}=200$). The black line represents the full complement of data encompassed within the manual gating regions, both labeled and unlabeled. The colored lines correspond to the final distributions of each of the separately labeled training data only (purple = ${}^{38}\mathrm{S}$, blue = ${}^{38}\mathrm{Cl}$, gray = ${}^{33}\mathrm{P}$, pink = ${}^{181}\mathrm{Ta}$). The yellow ($>0.25$), blue ($>0.60$), and pink ($>0.81$) vertical lines identify the lower-limit $k_{ml}$ integral values, where the upper limit was defined $=1$, applied throughout the $\gamma$-ray analysis (see text for additional details).

Figure 5

(a), (c), (e) Background-subtracted $\gamma$-ray singles spectra from a model output cut of $k_{ml}>0.6$ (blue) overlaid on a cut of $k_{ml}>0.25$ (yellow). All transitions belonging to ${}^{38}\mathrm{S}$ are labeled by their energies while those in bold have been newly determined in the present work. Parentheses indicate transitions that were unable to be placed in the level scheme (Fig. 6) and may be considered tentative. The recoil-$\gamma \text{−}\gamma$ spectrum ($k_{ml}>0.6$ cut) for each ${}^{38}\mathrm{S}$ transition labeled in panels (a), (c), and (e) were combined to generate the inclusive summed spectra shown in panels (b), (d), and (f). The blue vertical lines correspond to the labeled energies of the above histogram.

Figure 6

The level scheme of ${}^{38}\mathrm{S}$ based upon the present work and other in-beam measurements. Dashed levels and transitions indicate tentative placement. Transitions in blue ($L=2$) and purple ($L=1$) reflect multipolarities based on their $R_{{149}^{\circ }/{90}^{\circ }}$ values (Fig. 8 and Table 2).

Figure 7

Projected recoil-$\gamma \text{−}\gamma$ coincidence spectra for $k_{ml}>0.25$. The labels provide the $\gamma$-ray energy or energies selected for the projection. The “$+$” sign represents the summation of two separate recoil-$\gamma \text{−}\gamma$ spectra. Only some of the transitions of interest have been labeled in each spectra. No background subtractions have been applied.

Figure 8

The ratio of the extracted $\gamma$-ray yields centered around ${\theta }_2={149}^{\circ }$ by that around ${\theta }_1={90}^{\circ }, R_{{149}^{\circ }/{90}^{\circ }}$, for identified transitions in ${}^{38}\mathrm{S}$ as a function of their energy. The colored data points correspond to either fully stretched quadrupole transitions residing above $\approx 1.2$ (blue for multipolarity $L=2$) or dipole transitions residing below $\approx 1$ (purple for multipolarity $L=1$). Gray data points were not assigned multipolarities primarily due to large uncertainties.

Figure 9

A subset of the experimental excited-state levels in ${}^{38}\mathrm{S}$ are presented along with $J^{\pi }$ assignments where available. Those in blue emphasize the established yrast even-$J$ levels. Calculated levels based on the FSU [31] interaction in which the protons were confined to the $1s0d$ shell and neutrons to the $1p0f$ shell are labeled as 0p-0h. Those that allowed for one- or two particle-hole excitations across the $N=20$ shell gap, from within the $1s0d$ shell to the $0f1p$ shell, are labeled by 1p-1h or 2p-2h, respectively. Only a subset of the calculated levels are also shown (see text for additional details).

Figure 10

The excitation energies and calculated occupancies (0p-0h) of the even-$J^{+}$ yrast states in ${}^{38}\mathrm{S}$ through the ${10}^{+}$ level. The relative occupancies for the “last” three $sd$-shell protons and the two neutrons within the $0f1p$ shell are labeled by color and connected by lines to highlight their evolution. The five remaining $sd$-shell protons fill the $\pi 0d_{5/2}$ orbital and the occupancy is only for the “sixth” proton, i.e., an occupancy of one on the plot represents a filled $\pi 0d_{5/2}$ orbital ($0d_{5/2}{)}^6$ and a value of zero gives $\pi {\left(0d_{5/2}\right)}^{-1}$.

Figure 11

The even-$J^{+}$ yrast excitation energies ($E_x$) and $\nu 1{\mathrm{p}}_{3/2}$ occupancies from the 0p-0h shell-model calculations using the FSU interaction [31] (lines) for a selection of even $ZN=22$ isotones. The experimental energies for the $J^{\pi }=0_1^{+}$ (blue squares), $2_1^{+}$ (green circles), $4_1^{+}$ (pink triangles), and $6_1^{+}$ (purple diamonds) are also given [3].